1 / 22

Chapter 6

Chapter 6. Chapter 6.1 Law of Sines. In Chapter 4 you looked at techniques for solving right triangles. In this section and the next section you will solve oblique triangles . Oblique triangles are triangles that have no right angle.

desirae-klein
Télécharger la présentation

Chapter 6

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  1. Chapter 6

  2. Chapter 6.1 Law of Sines In Chapter 4 you looked at techniques for solving right triangles. In this section and the next section you will solve obliquetriangles. Oblique triangles are triangles that have no right angle. As standard notation, the angles of a triangle are labeled A, B,and C and their opposite angles are labeled a,b,and c. C Note: Angle A is between b and c, B is between a and c, C is between a and b. a b B A c

  3. Chapter 6.1 Law of Sines To solve an oblique triangle, you need to know the measure of at least one sideand the measures of any two other parts of the triangle- two sides, two angles, or one angle and one side. This breaks down into four cases: Two angles and any side (AAS or ASA) Two sides and an angle opposite one of them (SSA) Three sides (SSS) Two sides and their included angle (SAS)

  4. Derive Law of Sines

  5. Chapter 6.1 Law of Sines1 NOTE: The Law of Sines can also be written in the reciprocal form

  6. Example #1 GIVEN: Two Angles and One Side-AAS C=102.3°, B=28.7°, and b=27.4 feet Find the remaining angle and sides A=180° - B - C =180° - By the Law of Sines you have

  7. GIVEN: A=10°, a=4.5, B=60° Try #3 page 398 Use Law of Sines to Solve the triangle

  8. Example#2 GIVEN: Two Angles and One Side-ASA A pole tilts toward the sun at an 8° angle from the vertical, and it casts a 22 foot shadow. The angle of elevation from the tip of the shadow to the top of the pole is 43°. How tall is the pole?

  9. Try #27 page 398 Use Law of Sines to Solve the triangle

  10. The Ambiguous Case (SSA) If two sides and one opposite angle are given, three possible situations can occur: (1) no such triangle exists, (2) one such triangle exists, or (3) two distinct triangles satisfy the conditions

  11. Example #3 Single-Solution Case (SSA) One solution: a > b

  12. Try #15 page 398 Use Law of Sines to Solve the triangle

  13. Example #4 No-Solution Case – SSA Show that there is no triangle for which a = 15, b = 25, and A = 85º No solution a < h

  14. Try #17 page 398 Use Law of Sines to Solve the triangle

  15. Example #5 Two Solution Case Find two triangles for which a = 12 meters, b = 31 meters, and A = 20.5º

  16. Try #19 page 398 Use Law of Sines to Solve the triangle

  17. Area of a Oblique Triangle

  18. Example #6 Area of an Oblique Triangle Find the area of a triangular lot having two sides of lengths 90 meters and 52 meters and an included angle of 102°

  19. Try #21 page 398 Find the area of the triangle

  20. Example #7 An Application of the Law of Sines The course for a boat race starts at point A and proceeds in the direction S 52° W to point B, then in the direction S 40° E to point C, and finally back to A. Point C lies 8 kilometers directly south of point A. Approximate the total distance of the race course.

  21. Try #29 page 398 Use Law of Sines to Solve the triangle

  22. THEEND

More Related